Nucleon Energy Correlators (NECs) Overview

• Nucleon Energy Correlators (NECs) are operator-defined energy-weighted angular correlation observables that reveal the microscopic parton distribution and internal transverse dynamics of nucleons.
• They are measured in deep inelastic scattering experiments by tracking energy flow in target fragmentation without relying on non-perturbative fragmentation functions or jet algorithms.
• Extensions of NECs—including polarized, small-x, semi-inclusive, and jet-based formulations—enhance their applicability and deepen insights into nucleon internal structure.

Nucleon Energy Correlators (NECs) are operator-defined, energy-weighted angular correlation observables introduced to encode the microscopic details of a nucleon, including the parton angular distribution in a nucleon, the collinear splitting to all orders, and the internal transverse dynamics of the nucleon. In their original formulation, NECs are measured in lepton-nucleon deep inelastic scattering (DIS) through weighted energy flow in the target fragmentation region, without introducing non-perturbative fragmentation functions or jet clustering algorithms. Subsequent work developed polarized, small-$x$, semi-inclusive, and jet-based extensions, so the literature now uses both “nucleon energy correlators” and “nucleon energy-energy correlators” for closely related constructions (Liu et al., 2022, Cao et al., 2023).

1. Definition and operator structure

The basic NEC is built from a partonic bilocal operator with an insertion of the energy flow operator. A general quark $n$-point definition is

$$f_{q,n}(x,\{\Omega_i\}) = \int \frac{dy^-}{2\pi}\, e^{-ixy^-P^+} \left\langle P,s \left| \bar{\xi}(y^-,0)\,\mathcal{L}(\infty)\, \mathcal{E}(\Omega_1)\cdots \mathcal{E}(\Omega_n)\,\Gamma\, \mathcal{L}(\infty,0)\,\xi(0) \right| P,s \right\rangle ,$$

where $